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Abstract

This paper presents the mathematical foundations of Dirichlet mixtures, which have been used to improve database search results for homologous sequences, when a variable number of sequences from a protein family or domain are known. We present a method for condensing the information in a protein database into a mixture of Dirichlet densities. These mixtures are designed to be combined with observed amino acid frequencies, to form estimates of expected amino acid probabilities at each position in a profile, hidden Markov model, or other statistical model. These estimates give a statistical model greater generalization capacity, such that remotely related family members can be more reliably recognized by the model. Dirichlet mixtures have been shown to outperform substitution matrices and other methods for computing these expected amino acid distributions in database search, resulting in fewer false positives and false negatives for the families tested. This paper corrects a previously p...